AQ 232 – Fish Population Dynamics and Stock Assessment
Methods of Estimating Fish Stock Abundance
Nyamisi Peter
2026-01-30
2. Acoustic Surveys
The hydroacoustic survey uses an echo sounder to conduct acoustic biomass estimation.
It is widely used for assessing pelagic fish stocks (e.g., sardines, anchovies, herring, mackerel, tuna).
2. Acoustic Surveys
In practice for fish stock assessment, acoustic surveys are used to estimate fish stock.
These surveys are used to estimate the abundance of fish species that form schools in the water column.
They are particularly useful for pelagic species that are difficult to sample with traditional trawl surveys.
Acoustic Surveys: Key Terms
Acoustic survey - A survey that uses acoustic sound to estimate fish stock.
Echo sounder - A device that uses sound waves to detect fish.
Echo - A sound wave that is reflected back to the sounder.
Hydroacoustic survey - A survey that uses hydroacoustic sound to estimate fish stock.
Hydroacoustic means using sound in water.
Acoustic survey methodology
An acoustic transducer emits a brief, focused pulse of sound into the water.
If the sound encounters objects that are of different density than the surrounding medium, such as fish, they reflect some sound back toward the source.
The time it takes for the echo to return is used to calculate the distance to the object.
Acoustic survey methodology…
These echoes provide information on fish size, location, and abundance.
The basic components of the scientific echo sounder hardware function is to transmit the sound, receive, filter and amplify, record, and analyze the echoes.
While there are many manufacturers of commercially available fish-finders, quantitative analysis requires that measurements be made with calibrated echo sounder equipment, having high signal-to-noise ratios.
Principle of echo sounding
Everything scattered in the water column reflects sound waves depending on the frequency of the waves.
The higher frequency the shorter the wave length.
Therefore frequencies > 200 KHz can produce echo from plankton.
For fishes, a lower frequency < 200 KHz is used
Conditions for echo sounding
Suitable for small pelagic fish stocks (big pelagic fishes eg. Tuna swim very fast and therefore the method becomes unsuitable).
The behavior of the fish to be assessed must be known
e.g the distribution of the fish in the water column at different times
The reaction of the fish towards the fishing boat should also be taken into account.
The use of a smaller boat towed by the bigger vessel to carry the transducer helps to detect fish which are frightened by the vessel.
Limitations of echo sounders
Sound beam interference by sound scatters eg. temperature stratification, air bubbles, sediments, debris, vegetation
Unsuitable for very shallow depths because of the blind zone that exists a few meters below the transducer depending on the diameter of the transducer and the frequency of the sound waves.
The larger the diameter the larger the zone.
Very deep waters calls for a stronger pulse generating echo sounder
3. Underwater Visual Census Survey (UVCS)
The more traditional method in which diver count fish along transects
It involves an observer, equipped with SCUBA gear, estimating the abundance of fish within a given area (the belt transect).
A multitude of factors, including fish mobility and habitat complexity, have been shown to effect the precision of the counting technique.
Applications of UVCS
Best suited for:
- Reef fish communities
- Shallow coastal waters
- Clear water environments
- Surface schooling species (tuna, sardines)
Underwater Methods
Belt Transect Method:
Diver swims along fixed transect (e.g., 50 m × 5 m)
Records all fish within belt width
Estimates size classes
Multiple transects per site
Point Count Method:
Diver remains stationary
Counts fish within cylinder (e.g., 7.5 m radius)
Records species, size, abundance
Less affected by fish flight behavior
Advantages & disadvantages of UVCS
Advantages:
Direct observation
Species identification possible
Behavioral information
Relatively low cost
Good for complex habitats (reefs)
Disadvantages:
Limited to clear, shallow water
Weather and visibility dependent
Observer bias
Diver safety concerns
Small spatial coverage
Fish behavior affects counts
4. Catch per unit effort (CPUE)
CPUE is catch obtained per standardized unit of fishing effort
Used as an index of abundance (relative, not absolute)
Catch rate (CPUE) is frequently and single most useful index for long-term monitoring of a fishery
Changes in CPUE may give an indication of what is happening to the fish stock size
In theory, a constant trend of CPUE values represents a stable stock
A rising trend indicates an increasing stock
Increases in CPUE may mean that a fish stock is recovering and more fishing effort can be applied.
4. Catch per unit effort (CPUE)…
A falling trend signifies a declining stock
A declines in CPUE may mean that the fish population cannot support the level of harvesting.
However, a falling trend does not necessarily indicate overfishing;
A fish stock will always decline from its initial high level when fishing occurs until it reaches an equilibrium level, when productivity balances the catch being taken.
CPUE can therefore be used as an index of stock abundance
Advantages & disadvantages of CPUE
Advantages:
Uses existing commercial data
Cost-effective
Long time series available in many areas
Large spatial coverage
Real-time updates possible
Advantages & disadvantages of CPUE
Disadvantages:
Differences regarding interpretation of fishing effort
Changes in actual or effective effort as a result of technological development
Also influenced by skills, experience
Affected by fisher behavior
May not reflect true abundance
Reporting biases
It is also difficult to know what factors of the fishing operations are important to measure
It is difficult to keep up with fishery changes
eg. CPUE could be altered without it being reflected on the stock size
A boat may install a more powerful motor
Or change from day to night fishing.
Not useful for measuring changes in the stock size of schooling fish species
eg. a pelagic species which schools at the surface can be easily seen from fishing boats or spotter planes therefore can be caught in bulk by purse seine nets.
5. Mark-Recapture Methods
Is a Relative Fish abundance estimation
It involves capturing, marking, release and recapturing
The basic concept is that;
The ratio of recaptures in the second sample is equivalent to the proportion of those that were marked during the first sampling occasion to the whole population.
5. Mark-Recapture Methods…
Then, estimation of population size (N) will be;
\[
\frac{m_2}{n_2} = \frac{n_1}{N}
\]
Sample 1 – marked and released
\(n_1\) = number captured and marked on the 1st sampling occasion
Sample 2 - number of recaptures recorded
\(n_2\) = number captured on the second sampling occasion
\(m_2\) = number of recaptures on the second occasion
Assumptions for mark recapture method
The population is closed so that N remains constant
i.e. there is no movement in or out by birth, death, immigration or recruitment
All the fish have the same probability of being caught
Marked and unmarked fish have equal capture probability
The second sample is a random sample of the population
No marks of fish are lost between the sampling occasions
No marks go unrecorded during the second sampling
Marks do not affect survival
Advantages & disadvantages of Mark-Recapture
Advantages:
Direct abundance estimate
Provides movement information
Estimates survival rates
Useful for discrete populations
Disadvantages:
Tagging stress and mortality
Tag loss or shedding
Expensive and labor-intensive
Assumption violations is common
Limited to feasible population sizes
Mark-Recapture: Example 1
Problem:
500 tilapia are captured, marked, and released in Lake Victoria. One week later, 200 fish are recaptured, of these, 25 have marks. Find the population estimate in the lake.
Solution
Using the mark-recapture formula:
\[\frac{m_2}{n_2} = \frac{n_1}{N}\]
Where:
\(n_1 = 500\) (marked fish released)
\(n_2 = 200\) (fish recaptured)
\(m_2 = 25\) (marked fish recaptured)
\(N\) = ??? (unknown population size)
Rearranging the formula to solve for \(N\): \[N = \frac{n_1 \times n_2}{m_2}\] Substituting the values: \[N = \frac{500 \times 200}{25} = 4000\]
The estimated population size of tilapia in Lake Victoria is 4000 fishes.
Mark-Recapture: Example 2
In a capture-recapture process, 200 fishes were tagged. From the capture results, the game warden estimates that, the lake contains 2500 fishes. What percentage of fishes were tagged?
Solution
Let p be the percent of tagged fishes;
\[
\frac{n_1}{N} = \frac{p}{100}
\]
\(\frac{200}{2500}=\frac{p}{100}\)
\(p = 8\%\)
About \(8\%\) of fishes were tagged
6. Depletion Methods
This method is mainly used for shell fish fishery i.e Octopus
The method uses either of the two models i.e Leslie and DeLury methods which depend upon the following assumptions;
Fishing (or sampling) must take a significant proportion of the population causing a depletion
6. Depletion method…
The decrease in catch per unit effort is proportional to;
The reduction in the population
Catchability of fish remains constant
Units of effort (or fishing gear) do not compete with one another - remains the same
The entire population is available to the fishery
There is no recruitment, natural mortality, immigration or emigration in the population.
6. Depletion method…
It involves the removal of individuals from a stock and measuring the resulting decrease in relative abundance using CPUE as an abundance index.
It involves fishing on a closed population in which there is no immigration and emigration
Time interval is short enough to ignore losses due to natural mortality.
6. Depletion method…
Leslie Method:
\[
\frac{C_t}{f_t} = q(N_o - IC)
\qquad(1)\]
Where;
\(C_t\) = number of fish caught at time t
\(f_t\) = effort expended in taking \(C_t\)
\(\frac{C_t}{f_t}\) = catch per unit effort at time t (CPUE)
\(N_o\) = initial population size
\(q\) = catchability
\(IC\) = accumulated catch
6. Depletion method…
Or the Leslie formula can be expressed as;
\[
C_t = qN_0 - q\sum_{i=1}^{t-1}C_i
\qquad(2)\]
Where:
\(C_t\) = Catch in period \(t\)
\(q\) = Catchability coefficient
\(N_0\) = Initial population size
\(\sum_{i=1}^{t-1}C_i\) = Cumulative catch up to time \(t-1\)
# Fit linear regression: Catch vs Cumulative Catchleslie_model <-lm(catch ~ cumulative_catch, data = octopus_data)N0_estimate <-coef(leslie_model)[1]q_estimate <--coef(leslie_model)[2]# intercept = coef(leslie_model)[1]# q = coef(leslie_model)[2] #slope# from C_t = qN0 - q*IC# intercept = qN0# therefore N0 = intercept/q
Leslie graph
Advantages & disadvantages of depletion methods
Advantages:
Simple data requirements
Uses commercial fishing data
Provides absolute estimate
Quick results
Disadvantages:
Requires closed population
Needs significant depletion
Assumes constant catchability
Not suitable for mobile species
Short-term application only
7. Pelagic Egg and Larval Surveys
Principle:
Sample ichthyoplankton (fish eggs and larvae)
Estimate spawning stock biomass from egg production
7. Pelagic Egg and Larval Surveys..
Daily Egg Production Method (DEPM):
\[SSB = \frac{P_0 \times A}{R \times S \times F}\]
Where:
\(SSB\) = Spawning stock biomass
\(P_0\) = Daily egg production per unit area
\(A\) = Spawning area
\(R\) = Sex ratio (proportion female)
\(S\) = Spawning fraction (proportion spawning per day)
\(F\) = Batch fecundity (eggs per spawning female)
Parameter interpretation
\(P_0\) (Daily Egg Production): Measures spawning intensity in the survey area. Higher \(P_0\) indicates active spawning; reflects reproductive output per unit spawning habitat.
\(A\) (Spawning Area): Geographic extent of the spawning ground. Larger area = greater total egg production. Accurate delineation is critical.
\(R\) (Sex Ratio): Only females produce eggs. Must adjust for proportion of females in spawning population.
\(S\) (Spawning Fraction): Not all females spawn on a given day. Varies by species and environmental conditions. Lower \(S\) = smaller daily fraction of stock spawning.
\(F\) (Batch Fecundity): Individual female reproductive capacity. Higher \(F\) = fewer females needed to produce observed eggs. Critical parameter often determined from histological analysis.
Sample question 1:
A sardine spawning survey in Tanzanian coastal waters collected the following data:
Daily egg production per unit area (\(P_0\)) = 450 eggs/m²/day
Spawning area (\(A\)) = 5,000 km²
Sex ratio (\(R\)) = 0.52 (52% female)
Spawning fraction (\(S\)) = 0.35 (35% spawn per day)
Batch fecundity (\(F\)) = 12,000 eggs/female
Calculate the spawning stock biomass (SSB) of sardine given that each sardine egg weighs ~0.75 mg.